perimeter of suare / d ( diagonal ) = a / \sqrt{2}

perimeter of suare = a / \sqrt{2} * d

a ( side of square) = perimeter \sqrt{2} / d

a = a / \sqrt{2} * d * \sqrt{2} * 1 / a \sqrt{2} =

= ( 1 / \sqrt{2} * d * \sqrt{2} ) / \sqrt{2} = d / \sqrt{2}

knowing the proportion of perimeter of square to his side, count the proportion of perimeter of oval to perimeter of suare based on the same diagonal :

obw kwad / obw koła

perimeter of suare = a / \sqrt{2} * d ( diagonal )

perimeter of oval = 2 pi * d

a ( side) = perimeter \sqrt{2} / d

( a / \sqrt{2} * d ) / ( 2 pi * d ) = d / 2 pi

( i dont know if its good )